Animals in groups often exchange calls, in patterns whose temporal structure may be influenced by contextual factors such as physical location and the social network structure of the group. We introduce a model-based analysis for temporal patterns of animal call timing, originally developed for networks of firing neurons. This has advantages over cross-correlation analysis in that it can correctly handle common-cause confounds and provides a generative model of call patterns with explicit parameters for the influences between individuals. It also has advantages over standard Markovian analysis in that it incorporates detailed temporal interactions which affect timing as well as sequencing of calls. Further, a fitted model can be used to generate novel synthetic call sequences. We apply the method to calls recorded from groups of domesticated zebra finch (Taenopyggia guttata) individuals. We find that the communication network in these groups has stable structure that persists from one day to the next, and that "kernels" reflecting the temporal range of influence have a characteristic structure for a calling individual's effect on itself, its partner, and on others in the group. We further find characteristic patterns of influences by call type as well as by individual.